An algebraic construction is a method by which an algebraic entity is defined or derived from another.

Instances include:

This list is incomplete; you can help by adding missing items. (February 2011)

• Cayley–Dickson construction
• Proj construction
• Grothendieck group
• Gelfand–Naimark–Segal construction
• Ultraproduct
• ADHM construction
• Burnside ring
• Simplicial set
• Fox derivative
• Mapping cone (homological algebra)
• Prym variety
• Todd class
• Adjunction (field theory)
• Vaughan Jones construction
• Strähle construction
• Coset construction
• Plus construction
• Algebraic K-theory
• Gelfand–Naimark–Segal construction
• Stanley–Reisner ring construction
• Quotient ring construction
• Ward's twistor construction
• Hilbert symbol
• Hilbert's arithmetic of ends
• Colombeau's construction
• Vector bundle
• Integral monoid ring construction
• Integral group ring construction
• Category of Eilenberg–Moore algebras
• Kleisli category
• Adjunction (field theory)
• Lindenbaum–Tarski algebra construction
• Freudenthal magic square
• Stone–Čech compactification